Ground state solution for fractional p-Choquard equations with upper critical exponent

Abstract

In this paper, we investigate the following fractional p-Choquard equations with upper critical exponent involving two potentials:(−Δ)psu+V(x)|u|p−2u=[Iα⁎|u|ps,α⁎]|u|ps,α⁎−2u+K(x)f(x,u),x∈RN, where N⩾1, 0<s<1, 2⩽p<Ns, ps,α⁎=p(N+α)2(N−ps), Iα is the Riesz potential of order α∈(0,1), the potentials V,K:RN→R and nonlinearity f:RN×R→R are continuous functions satisfying some natural hypotheses. We show the existence of a ground state solution to above equations when V and f are periodic and asymptotically periodic in x, respectively, by using the idea of Nehari manifold technique and the Lions' concentration compactness principle.